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Abstract

Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device. In this paper we demonstrate 10× temporal super resolution with multiple depths recovery from a single image. Two examples are presented for the purpose of recording subtle vibrations and tracking small particles within 5 ms.

Figures (6)

Fig. 1 4D holographic model. E0(x, y, t; z0): projection of a 4D field at z0, the n-th depth plane has a distance of dn to z0; M(x, y, t): temporal coded mask located at z1; G(x, y, Δt): captured image with an integral over Δt. The sensor is located at z2.

Fig. 4 Performance simulations. (a) Scenario: two Peranema with different sizes moving at different planes (dz), a single image is simulated at the sensor plane; (b) Space-time performance. Horizontal axis indicates different spacing between the two objects. “100%”: full resolution; “50%”: 50% of the pixels are randomly sampled at each time frame, which corresponds to a temporal increase of 2; “20%”: temporal increase of 5; “10%”: temporal increase of 10. Lines represent CS results and dashed lines represent BP results. PSNR in dB. (c) Reconstruction results at depth d1. Marked as red circle in (b).